This is ?
The partial derivatives of with respect to u and v are
That is, just take the partial derivatives of the integrand.
I'm trying to understand Fourier series and in order to do so have to be able to calculate the partial derivates of the function:
I_n=(Integral [ f(x) - a_0/2 - sigma (a_k cos(kx) + b_k sin(kx)]^2)dx
w.r.t. a_0, a_k and b_k, where the integral is calculated from -pi to pi.
I actually had certain thoughts about how to go about this, which I originally wrote here, but as I quickly realized it was completely wrong I've deleted this... Now I'm thinking like this: it's a definite integral, so if I calculate the primitive functions of all the terms containing x, and then calculate the partial derivatives that should do it, no?
Still, I don't get the answer in my book... So....
If someone could explain to me how to go about this in an easy-to-understand, step-by-step manner it'd be greatly appreciated!